%0 Journal Article
%T Dense subgraphs in the H-free process
%A Lutz Warnke
%J Mathematics
%D 2010
%I arXiv
%R 10.1016/j.disc.2011.08.008
%X The H-free process starts with the empty graph on n vertices and adds edges chosen uniformly at random, one at a time, subject to the condition that no copy of H is created, where H is some fixed graph. When H is strictly 2-balanced, we show that for some c,d>0, with high probability as $n \to \infty$, the final graph of the H-free process contains no subgraphs F on $v_F \leq n^{d}$ vertices with maximum density $\max_{J \subseteq F}\{e_J/v_J\} \geq c$. This extends and generalizes results of Gerke and Makai for the C_3-free process.
%U http://arxiv.org/abs/1003.0220v2